The collision between water and stone, stone-skipping science

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iVenky
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I am trying to understand the science of stone skipping.

First, if the stone is thrown vertically would it bounce at least once for any possible velocity or does it go down only?
What sort of collision is it when the stone touches the water and how to look at conservation of momentum in this case of stone skipping?
 
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ZapperZ said:
Thanks, that really helped me. I read the papers. I am trying to understand why the author mentions (in paper 1) "the stone will rebound if it stays only partially immersed during the collision" at the beginning of page 3. And he mentions a condition |z| < a sin Θ. Does this mean even if I drop the stone vertically from a height, then Θ=0 which means it would never rebound? My confusion, wouldn't there still be a rebound force caused by the impact force > it's own mass so it should still be able to bounce (just like a ball dropped from a height on the ground). What am I doing wrong here?